Johnna J. Bolyard

A Review of the Literature on Mathematics and Science Teacher Quality

A large body of literature exists that examines teacher quality characteristics and the relationship of indicators of those characteristics to teacher effectiveness. This existing research literature broadly views teacher quality research without illuminating specific areas of teacher quality, such as mathematics and science. In an effort to focus the literature base for researchers and policymakers more narrowly, this review specifically examines teacher quality as it relates to mathematics and science teaching and learning. The review highlights key policy and practitioner perspectives, provides a focused synthesis on current research findings on mathematics and science teacher quality, and suggests areas of research that are limited in the literature.

Revisiting the Definition of a Virtual Manipulative

In 2002, Moyer, Bolyard and Spikell defined a virtual manipulative as an “an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge” (p. 373). The purpose of this chapter is to revisit, clarify and update the definition of a virtual manipulative. After clarifying what a virtual manipulative is and what it is not, we propose an updated definition for virtual manipulative: an interactive, technology-enabled visual representation of a dynamic mathematical object, including all of the programmable features that allow it to be manipulated, that presents opportunities for constructing mathematical knowledge. The chapter describes the characteristics of five of the most common virtual manipulative environments in use in education: single-representation, multi-representation, tutorial, gaming and simulation.

Common features of professional development activities for mathematics and science teachers

This study examines professional development activities provided for mathematics and science teachers in the National Science Foundation’s Math and Science Partnership Program by analyzing a cross‐sectional sample of over 2000 professional development (PD) activities in the program. Data were gathered from secondary source documents and surveys to examine core and structural features of professional development offerings (i.e. form, collective participation, content, duration and outcomes). The results from this sample of PD activities for mathematics and science teachers were mixed. There was evidence of research‐based practices, including the collective participation by teachers at the same grade levels, a focus on content‐specific training and sufficient duration. However, courses and workshops continued as the dominant form of PD delivery, there are few measures used to assess the PD activities, and the partnerships did not connect PD efforts for mathematics and science teachers with classroom practices and student achievement outcomes. These findings indicate that the delivery of PD has adopted important research‐based strategies, but that the partnerships need to design better methods for documenting growth in teacher knowledge and connecting that growth with student outcomes.

Multilayered knowledge: understanding the structure and enactment of teacher educators’ specialized knowledge base

In order to corroborate and grow teacher educator knowledge (TEK) scholarship, this paper describes an in-depth-focused exploration of a group of teacher educators providing professional development. Our grounded data analysis allowed us to define different major elements, sub-elements, and components that comprise TEK, as well as make explicit how the use of this knowledge—in the context of teaching professional development—draws upon multiple components at any given moment. These findings hold implications for TEK scholarship and practice. Specific to scholarly efforts, while current models for TEK are useful for explicating common understandings amongst the research community, the most functional representations should be fluid and dynamic, in part by balancing both breadth and depth in their scope. Specific to the development of teacher educators, teacher educator preparation should recognize, emphasize, and develop future teacher educators’ layered understandings (i.e. knowledge of students and teachers) and robust knowledge of contexts.

Second-Graders' Mathematical Practices for Solving Fraction Tasks.

Abstract Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children’s mathematical practices through an exploratory examination of the practices of a group of second-grade students engaged in several mathematical tasks focused on rational number concepts. Twenty-five second-grade students completed three fraction tasks in structured clinical interviews. The interviews and student work were analyzed using an interpretational analysis to examine the data for constructs, themes, and patterns that were useful in explaining children’s mathematical practices. The results reveal that children used a variety of mathematical practices during the interviews to respond to the mathematical problems presented. Children’s mathematical practices were both a product that they used to solve the mathematical situations, and a process that was developing during the interactions of the interview. The findings lead to new insights about how mathematical practices develop and what promotes their development.